Question Number 112805 by Aina Samuel Temidayo last updated on 09/Sep/20 $$\mathrm{If}\:\mathrm{x}=\frac{\sqrt{\mathrm{a}+\mathrm{2b}}+\:\sqrt{\mathrm{a}−\mathrm{2b}}}{\:\sqrt{\mathrm{a}+\mathrm{2b}}−\:\sqrt{\mathrm{a}−\mathrm{2b}}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{bx}^{\mathrm{2}} −\mathrm{ax}+\mathrm{b}\:\mathrm{is} \\ $$ Answered by nimnim last updated on 09/Sep/20 $$\:\:\:\:\:\frac{\mathrm{x}}{\mathrm{1}}=\frac{\sqrt{\mathrm{a}+\mathrm{2b}}+\sqrt{\mathrm{a}−\mathrm{2b}}}{\:\sqrt{\mathrm{a}+\mathrm{2b}}−\sqrt{\mathrm{a}−\mathrm{2b}}}…
Question Number 112803 by Aina Samuel Temidayo last updated on 09/Sep/20 $$\mathrm{If}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{0},\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{yz}}\:\mathrm{is} \\ $$ Answered by MJS_new last updated…
Question Number 178338 by Acem last updated on 15/Oct/22 $${Let}\:{S}=\:\left\{\mathrm{1},\:\mathrm{2},\:…,\:\mathrm{9},\:\mathrm{0}\right\}\:\boldsymbol{{A}}:\:{How}\:{many}\:{multiples} \\ $$$$\:{of}\:{eight}\:{of}\:{four}\:{digits}\:{can}\:{be}\:{formed}\:{from}\:{S} \\ $$$$\:\boldsymbol{{B}}:\:{The}\:{same}\:{question}\:{for}\:{different}\:{digits} \\ $$ Commented by Acem last updated on 17/Oct/22 $$\boldsymbol{{Hint}}: \\…
Question Number 112796 by nimnim last updated on 09/Sep/20 $${For}\:{any}\:{real}\:{numbers}\:{x},{y}\:{and}\:{z}\:{if} \\ $$$${x}+{y}+{z}=\mathrm{2},\:{then}\:{prove}\:{that} \\ $$$${xyz}\geqslant\mathrm{8}\left(\mathrm{1}−{x}\right)\left(\mathrm{1}−{y}\right)\left(\mathrm{1}−{z}\right). \\ $$ Commented by nimnim last updated on 10/Sep/20 $$\mathrm{Yes}\:\mathrm{sir}.. \\…
Question Number 112795 by I want to learn more last updated on 09/Sep/20 Commented by MJS_new last updated on 10/Sep/20 $$\mathrm{trying}\:\mathrm{10}\leqslant{N}\leqslant\mathrm{99}\:\mathrm{we}\:\mathrm{get} \\ $$$${N}\in\left\{\mathrm{12},\:\mathrm{24},\:\mathrm{36},\:\mathrm{48},\:\mathrm{75},\:\mathrm{81}\right\} \\ $$…
Question Number 178320 by Shrinava last updated on 15/Oct/22 Commented by mr W last updated on 15/Oct/22 $${only}\:{if}\:\mathrm{log}\:\mathrm{3}\:{means}\:\mathrm{log}_{{e}} \:\mathrm{3},\:{i}.{e}.\:\mathrm{ln}\:\mathrm{3} \\ $$ Commented by Acem last…
Question Number 47239 by JDlix last updated on 06/Nov/18 $$\frac{\mathrm{1}.\mathrm{8}×\mathrm{10}^{\mathrm{6}} }{{tan}\left(\mathrm{89}.\mathrm{9999}°\right)}\:\sim\:\pi\:\left({upto}\:\mathrm{9}\:{decimal}\:{places}\right) \\ $$$${can}\:{i}\:{have}\:{some}\:{explanations}\:{how}\:{it}\:{is}\:{worked}\:{out}\:? \\ $$$${Thank}\:{you}! \\ $$ Commented by MJS last updated on 07/Nov/18 $$\mathrm{I}\:\mathrm{guess}\:\mathrm{somebody}\:\mathrm{just}\:\mathrm{messed}\:\mathrm{around}\:\mathrm{a}\:\mathrm{bit}.…
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Question Number 47179 by peter frank last updated on 05/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 06/Nov/18 $${eqn}\:{circle}\:\left({x}−\alpha\right)^{\mathrm{2}} +\left({y}−\beta\right)^{\mathrm{2}} ={r}^{\mathrm{2}} \\ $$$${since}\:{it}\:{touch}\:{y}\:{axis}\:\:{so} \\ $$$${radius}\:{r}=\alpha \\…
Question Number 178251 by mr W last updated on 14/Oct/22 $${solve} \\ $$$$\left({x}^{\mathrm{2}} −\mathrm{5}\right)^{\mathrm{2}} −{x}=\mathrm{5} \\ $$ Answered by BaliramKumar last updated on 14/Oct/22 $$\left({x}^{\mathrm{2}}…